SOLUTION: Theformula t=1/c [1n A-1n(A-N)] descibes the time t, in weeks, that it takes to achieve mastery of a portion of a task, where A is the maximum learning possible, N is the portion

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Question 259316: Theformula t=1/c [1n A-1n(A-N)]
descibes the time t, in weeks, that it takes to achieve mastery of a portion of a task, where A is the maximum learning possible, N is the portion of the learning that is to be achieved, and c is a constant used to measure an individuals learning style.
a. Express the formula so that the expression in brackets is written as a single logarithm.
b. The formula is also used to determine how long it will take chimpanzees and apes to master a task. For example, a typical chimpanzee learning sign language can master a maximum of 65 signs. Use the form of the formula from part (a) to answer this question: How many weeks will it take a chimpanzee to master 30 signs if c for that chimp is 0.03?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I am not familiar with this formula. I am going to assume that it is
t+=+%281%2Fc%29%28ln%28A%29+-+ln%28A-N%29%29
If this is not correct, then perhaps what follow will help you figure the correct solution. If not, then repost your question and put parentheses around each numerator and denominator.

a) Combining the two logarithms is simple if you know the appropriate property of logarithms: log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29. Using this on your formula we get:
t+=+%281%2Fc%29%28ln%28A%2F%28A-N%29%29%29

b) The solution to this part is to use the formula. You are told that the maximum task is to master 65 signs, This is our value for A. The goal is for the chimpanzee is to learn 30 signs. This is our value for N. And you are told that the value for c for a chimpanzee is 0.03. Substituting these values into the formula we get:
t+=+1%2F%280.03%29%28ln%2865%2F%2865-30%29%29%29
Simplifying this we get:
t+=+1%2F%280.03%29%28ln%2865%2F35%29%29
t+=+1%2F%280.03%29%28ln%281.8571428571428571%29%29
t+=+1%2F%280.03%29%280.6190392084062234%29
t+=+33.3333333333333333%280.6190392084062234%29
t+=+20.6346402802074467
(You are welcome to round these numbers off as desired.) From the formula and the information we were given, it will take a chimpanzee nearly 21 weeks to master 30 of the 65 signs.